arXiv:1202.6171v1 [astro-ph.SR] 28 Feb 2012 yboi oa uniaieycmae ihclassical with study to compared novae. difficult quantitatively been novae has symbiotic it X-ray. circumstances, and these Under UV such and including ob- outbursts, spectroscopic, observations obtain the photometric, multi-wavelength continuous to of and easy period dense not whole as is a it of more) data or differ- servational to years (one this of evolution-timescales Sge. why long tens very reason several HM to the Due and unknown arises. 475, ence still second however, HBV The is, Cyg, Vul. It PU in- V1016 and subgroup Tel, include RR first subgroup Ser, RT The duration Peg, short AG a very clude 1994). a and has begins Nussbaumer maximum, is, (M¨urset phase there & an optical nebular if underwent phase,” the a “supergiant star after group, ex- immediately second the group the almost when resem- In first supergiant phase,” The Symbi-outburst. “supergiant A-F years) accord- (RG). an (several subgroups evolutions. giant bling long two spectral red a into their a hibit divided and to be WD ing can systems a novae binary of otic in (WDs) consist dwarfs that white on occurring ena eateto at cec n srnm,Cleeo rsa Arts of College Astronomy, and Science Earth of Department [email protected] mn yboi oa,P u sarr xeto.It exception. rare a is Vul PU novae, symbiotic Among phenom- runaway thermonuclear are novae Symbiotic rpittpstuigL Journal using Astrophysical typeset the Preprint in appear to VLTO FTESMITCNV UVL–OTUSIGWIEDW WHITE OUTBURSTING – VUL PU NOVA SYMBIOTIC THE OF EVOLUTION UVul PU h Dcmoetdmntsi h a ekwietenbledominat nebulae the while log peak to rises flat WD M- the the its in (WD), of dominates dwarf temperature mo white component Our outbursting WD decline. an slow The i.e., a by emission, followed of peak components optical flat long-lasted a shows -as ercmedXryosrain rudJn 04whe headings: Subject st 2014 June is around burning observations minimum. hydrogen X-ray that recommend suggesting we WD, X-rays, the surrounding nebula ewe h 90ad19 ciss eoti h reddening the obtain We eclipses. decrea 1994 photosphere WD and the 32 1980 that M confi spanned the We confirmed that the WD. analysis between estimates, of the observational eclipse nebula to new our pulsating by associated unocculted Also Vul the nebula an PU by occulted of is partially occulted model one a WD is emission; the other nebular of the eclipses the total of be sources to eclipses 1994 epeetacmoielgtcremdlo h yboi oaP V PU nova symbiotic the of model light-curve composite a present We d 1. ∼ A INTRODUCTION 4 T . E p.W nepe h eetrcvr fbihns ntrsof terms in brightness of recovery recent the interpret We kpc. 7 tl mltajv 5/2/11 v. emulateapj style X eateto srnm,Ki nvriy ioh,Yokoha Hiyoshi, University, Keio Astronomy, of Department iais yboi oa aalsi aibe tr:idvda ( individual stars: — variables cataclysmic nova, — symbiotic binaries: tr:lt-ye—utailt tr ht dwarfs white — stars ultraviolet: — late-type stars: .Cpriu srnmclCne,Bryk 80-1 War 18,00-716 Bartycka Center, Astronomical Copernicus N. USTN E IN COMPANION GIANT RED PULSATING oapa nteAtohsclJournal Astrophysical the in appear to T (K) onaMiko lajewska Joanna & zm Hachisu Izumi aioKato Mariko ABSTRACT 4 . ,sgetn t Doii.W nlz h 90and 1980 the analyze We origin. WD its suggesting 5, dSine,Uiest fTko oaa euok,Tokyo Meguro-ku, Komaba, Tokyo, of University Sciences, nd Japan and sa cisn iayo h ria period orbital the of binary eclipsing an is h pia a eka ela h Vlgtcre and curve, light UV ( the reproduces mass as that WD well Vul as the PU peak estimated pre- of flat first opti- optical model (2011) the dense theoretical al. have a et sented we Kato Recently, as and observations. well UV as 1979 data in spectroscopic/photometric cal outbursted study. quantitative During Vul for chance dif- good PU 2011). a occulted offers Vogel are This & al. ferently. components Nussbaumer et emission Shugarov 1995; different 1996; eclipses, al. Garnavich et 1996; (Kolotilov yr) (13.4 in5 eaayelgtcre ftetoelpe and eclipses brightnesses two the the as well of as curves parameters Sec- light binary In the WD. analyze obtain the we observational of 5, new radius tion and our compares temperature 4 with of Section curves estimates 3. light Section theoretical extinction in Vul the our PU constrain to Using we distance Vul. curves, and PU light 2 of theoretical Section model (RG) our evolution 1994). component and our (1980 introduces cool hot eclipses briefly the two the the as of from well radius derived as and on based (WD), temperature nebulae, the component and of RG, estimates WD, new the of components sion were components emission other com- the outbursting neglected. the and of (WD) curve light ponent the for only however, hspprpeet opeesv oe femis- of model comprehensive a presents paper This bopinb eta yrgnis hydrogen neutral by absorption n E r ftetmeaueadradius. and temperature the of yr, a2382 Japan 223-8521 ma ( l on n odtc supersoft detect To on. going ill B e ytoodr fmagnitude of orders two by sed l(oaVleua 99 that 1979) Vulpeculae (Nova ul in opno,adnebulae. and companion, giant e ih-uv ossso three of consists light-curve del zw,Poland szawa, mdortertcloutburst theoretical our rmed − -in opno ihtwo with companion M-giant gatsco-idoii and origin cool-wind -giant’s V ) fe h photospheric the after e ∼ ∼ 0 . 0 R,NBLE AND NEBULAE, ARF, n itneto distance and 3 cis ftehot the of eclipse . 6 M ⊙ UVl — Vul) PU .Termdlis, model Their ). ∼ IUE/HST 90days 4900 153-8902, 2 Kato et al. of the RG and nebulae. Using these values, we construct WD. Therefore, the WD develops a helium layer under- a composite light curve model of PU Vul in Section 6. neath the newly accreted material. In the next outburst, Discussion and conclusions follow in Sections 7 and 8. a part of the helium layer will possibly be dredged up and mixed into the upper hydrogen layer. In such a case the 2. MODEL OF WD COMPONENT envelope will become helium-rich like in Models 3 and 4 2.1. Evolution of Nova Outbursts in Table 1. There are observational evidences of wind mass-loss A nova is a thermonuclear runaway event on a WD. Af- from WDs in some symbiotic stars. For PU Vul, ter the hydrogen shell flash sets in, the envelope on the Tomov et al. (1991) found broad emission wings in H I, WD expands to a giant size. After it reaches the optical He I, He II and N IV lines as well as violet-shifted P peak, the envelope settles down into a steady-state. The Cygni type absorption components in H I and He I lines optical magnitude decays as the envelope mass decreases in the optical spectra taken in 1990-91, which they at- while the photospheric temperature rises with time. The tributed to the hot component winds. Sion et al. (1993) decay phase can be followed by a quasi-static sequence discussed the onset of Wolf-Rayet type wind outflowing (Kato et al. 2011). We solved the equations of hydro- from the hot component based on the IUE high resolu- static balance, continuity, radiative diffusion, and conser- tion spectra of 1989-1991, and estimated an upper limit vation of energy, from the bottom of the hydrogen-rich −5 −1 of M˙ wind . 10 M⊙ yr . For AG Peg, the outburst envelope through the photosphere. The evolution is fol- lasted about 150 yr, which suggests a low mass WD lowed by a sequence of decreasing envelope mass. The with no optically-thick winds. The wind mass-loss rate time interval ∆t between two successive solutions is cal- from the hot component was estimated to be of the or- culated by ∆t = ∆Menv/(M˙ nuc + M˙ wind), where ∆Menv −7 −1 der of 10 M⊙ yr (Vogel & Nussbaumer 1994) and is the difference between the envelope masses of the two −6 −1 ˙ 10 M⊙ yr (Kenyon et al. 1993). The intensity of successive solutions, and Mnuc is the hydrogen nuclear the wind diminished in step with the hot component lu- ˙ burning rate and Mwind is the optically-thin wind mass- minosity during the decline of the outburst. For AE loss rate (see Equation (24) in Kato & Hachisu 1994, Ara, the wind mass loss rate is estimated to be a few −8 −7 −1 for more detail). The method and numerical techniques times 10 – 10 M⊙ yr and the WD mass to be are essentially the same as those in Kato et al. (2011). Mh sin i ∼ 0.4 M⊙ (Mikolajewska et al. 2003). We used OPAL opacities (Iglesias & Rogers 1996). The With such poor information on mass-loss rates, we WD radius (the bottom of hydrogen shell-burning) is as- simply assume that an optically-thin wind begins to sumed to be the Chandrasekhar radius. The mixing- blow when the photospheric temperature rises to log Tph length parameter of convection α is assumed to be 1.5 (K) ∼ 4.0 and the wind continues until log Tph (K) (see Kato & Hachisu (2009) for the dependence of the ∼ 5.05 at various rates listed in Table 1 (e.g., M˙ = light curve on α). Internal structures of the envelope are wind × −7 −1 essentially the same as those in Figure 7 of Kato et al. 5.0 10 M⊙ yr for Model 1). After the temperature ∼ (2011). We calculate optical and UV light curves from reaches log Tph (K) 5.05, the wind mass-loss rate drops ˙ −7 −1 the blackbody spectrum with the photospheric tempera- to Mwind ∼ 1.0 × 10 M⊙ yr . ture, Tph. To calculate V magnitude, we use the standard We cannot accurately determine the WD mass of PU Johnson V bandpass and add a bolometric correction of Vul only from our light curve analysis. Kato et al. 0.17 mag (see Section 4). (2011) obtained a plausible range of the WD mass, 0.5 In our model, we simply assume uniform chemical com- – 0.72 M⊙ corresponding to a reasonable range of the position of the envelope. PU Vul does not show any wind mass-loss rates. In the present paper, we adopt an CO/Ne enrichment but the overall chemical composition 0.6 M⊙ WD as a standard model of PU Vul (see Section is almost consistent with being solar; slightly subsolar 2.2 for more detail). of iron (Belyakina et al. 1984, 1989) and helium over- 2.2. Continuum UV Light Curve abundance (Andrillat & Houziaux 1994; Luna & Costa 2005) are reported. Thus, we assume four different sets In classical novae, a narrow spectral region around of chemical composition (X, Y , Z) by weight for hydro- 1455 A˚ is known to be emission-line free and can gen, helium, and heavy elements of the envelope as (0.7, be a representative of continuum flux (Cassatella et al. 0.29, 0.01), (0.7, 0.28, 0.02) (0.5, 0.49, 0.01), and (0.5, 2002). This continuum band has been used to determine 0.49, 0.006). Here Z = 0.01 is closer to the recent esti- distances to several classical novae (Hachisu & Kato mate of heavy element abundance of solar composition 2006; Hachisu et al. 2008; Kato et al. 2009), and also (Z =0.0128: Grevesse 2008). The WD mass is assumed used in analysis of PU Vul (Kato et al. 2011). As PU to be 0.6 M⊙ as listed in Table 1. Model 4 in Table 1 is Vul shows much weaker emission lines in its spectra than the same as Model 2 in Kato et al. (2011). classical novae, we can use three other wavelength bands A typical classical nova shows heavy element enrich- around 1350, 1490 and 1590 A˚ ofa20 A˚ width, in ment (C, O, and Ne) in its ejecta, which is interpreted in addition to the UV 1455 A˚ band. Figure 1 depicts light terms of dredge-up of WD material (Prialnik & Kovetz curves of these four narrow bands, extracted from the 1984, 1995). PU Vul shows no indication of such en- IUE data archive1. hancement in spectra, which suggests that the WD is During the outburst, the photospheric temperature not eroded during and before the outburst. The theoret- gradually rises and the photospheric radius shrinks while ical model described in Kato et al. (2011) showed that the bolometric luminosity is almost constant. Thus, a only a small part of the accreted matter was lost in the UV light curve has the peak at a certain temperature. optically-thin wind, and the rest was burned to helium due to hydrogen nuclear burning and accumulated on the 1 http://sdc.laeff.inta.es/ines/ PU Vul–evolution of WD, RG, and nebula 3
TABLE 1 Model Parameters
Subject Model 1 Model 2 Model 3 Model 4 Units X ... 0.7 0.7 0.5 0.5 Y ... 0.29 0.28 0.49 0.494 Z ... 0.01 0.02 0.01 0.006 WD mass ... 0.6 0.6 0.6 0.6 M⊙ a Mbol ... −5.44 −5.36 −5.63 −5.68 mag b MV,peak ... −5.61 −5.53 −5.80 −5.85 mag a 37 −1 Lpeak ... 4.6 4.2 5.5 5.7 10 erg s c maximum radius ... 63 60 61 64 R⊙ −5 initial envelope mass ... 4.0 2.6 3.4 4.6 10 M⊙ d −7 −1 H-burning rate ... 1.7 1.6 2.9 3.0 10 M⊙ yr e −7 −1 assumed wind mass-loss rate (T < 5.05) ... 5.0 3.0 2.0 3.0 10 M⊙ yr f −7 −1 assumed wind mass-loss rate (T > 5.05) ... 1.0 1.0 1.0 1.0 10 M⊙ yr a Typical values of the optical flat peak at log Tph (K) =3.9. b We adopt Mbol − 0.17 mag. c The radius reached before log Tph (K) =3.9. d Values at log Tph (K) =4.5. e Optically-thin wind from log Tph(K) = 4 to 5.05. f Optically-thin wind from log Tph(K) = 5.05 to the end of hydrogen burning. Figure 1 also shows theoretical UV light curves that rep- in Table 2 for four specified chemical compositions. This resent continuum emission in each wavelength. These table also shows a range of the bolometric luminosities four light curves show basically a similar behavior, be- at the optical flat peak. The larger the bolometric lumi- cause each wavelength is close. In a shorter wavelength nosity, the more massive the WD. Combining these the- band, the UV flux reaches maximum slightly later than oretical bolometric luminosities with the observed mag- in the other longer bands as indicated by upward arrows. nitudes, we can derive a range of the distance moduli, The flux at the observed peak is obtained to be F1350 = (m − M)V , which are shown in the last column of Table −13 −13 −13 5.7 × 10 , F1455 = 5.6 × 10 , F1490 = 6.7 × 10 , 2. −13 −1 −2 −1 and F1590 = 6.1 × 10 erg s cm A˚ , respectively. If the emission can be approximated by blackbody, un- 3. EXTINCTION AND DISTANCE absorbed peak fluxes should be larger in a shorter wave- Before deriving physical parameters of the nova, length band, while the absorbed fluxes are in the inverse we must estimate the extinction and distance. The order. Comparing these peak fluxes, we see that the reddening was estimated by various methods, H I 1455 A˚ band flux is too small, because the peak flux is Balmer line ratios, He II emission line ratios, in- more absorbed by cool winds from the M giant compan- terstellar optical/UV absorption features, and com- ion than in the other three bands of 1350, 1490 and 1590 parison between the observed optical/near-IR spec- A˚ (Shore & Aufdenberg 1993). The excess of F1490 may tra and some standards (Belyakina et al. 1982b, 1984; be explained by contamination of emission lines. Con- Friedjung et al. 1984; Kenyon 1986; Gochermann sidering these effects, we use the 1590 A˚ band in the 1991; Vogel & Nussbaumer 1992; Hoard et al. 1996; following discussion. Rudy et al. 1999; Luna & Costa 2005). They are un- Figure 1 also shows model light curves of the 0.6 M⊙ fortunately scattered in a broad range of E(B − V ) = WD with the chemical composition of X = 0.7, Y = 0.22−0.53. Thus, we have made our own estimates based 0.29, and Z =0.01. Each band light curve is made from on the theoretical light curves (Section 3.1) and compar- blackbody emission of our evolution model. Here, we ison between spectral classification and colors (Section assume four optically-thin wind mass-loss rates of 4–8 3.2). −7 −1 ×10 M⊙ yr . For a higher mass-loss rate, the evolu- tion is faster and the UV light curve shape is narrower. 3.1. Extinction from Model Light Curves All these light curves more or less agree with the obser- From our light curve fittings, we get relations on the vational UV light curve in each wavelength band, and we − −7 −1 extinction E(B V ) and the distance d to PU Vul. The chose the 5×10 M⊙ yr as having the best agreement distance modulus is with these data points. For a given chemical composition Kato et al. (2011) (m − M)V = AV + 5 log (d/1 kpc)+10, (1) obtained a range of the WD mass that reasonably well reproduces the UV light curve for reasonable rates of where AV = RV × E(B − V ) and RV =3.1. In the op- the optically-thin mass-loss. The lowest WD mass is ob- tical maximum phase, 1979-1986, except the eclipse, the −6 ± tained for a very large wind mass-loss rate of 1×10 M⊙ mean magnitude is obtained to be V = 8.59 0.06 (see yr−1, while the highest WD mass is for no wind mass- Table 4), whereas the absolute bolometric magnitude is loss. For example, if we fix the chemical composition Mbol = −5.44 from Model 1 (Table 1). Here, we adopt a to be X = 0.7 and Z = 0.01, a plausible WD mass is bolometric correction of BC(V )=0.17 (see Section 4), as between 0.52 and 0.72 M⊙, corresponding to the wind a representative value for an extended WD photosphere −6 −1 mass-loss rate of 1 × 10 M⊙ yr and no mass-loss, re- during the A-F spectral phase. Then, we have spectively. These ranges of the WD mass are summarized 14.20=3.1 × E(B − V ) + 5 log (d/1 kpc)+10. (2) 4 Kato et al.
TABLE 2 Range of Distance Moduli
a b c Composition WD Mass Lbol Vpeak − MV 37 −1 (X,Y,Z) (M⊙) (10 erg s ) (0.7, 0.29, 0.01) ... 0.52 – 0.72 3.4 – 6.1 13.87 – 14.52 (0.7, 0.28, 0.02) ... 0.5 – 0.67 3.0 – 5.0 13.75 – 14.30 (0.5, 0.49, 0.01) ... 0.5 – 0.62 3.0 – 5.7 14.03 – 14.45 (0.5, 0.494, 0.006) ... 0.53 – 0.65 4.5 – 6.5 14.19 – 14.58
a A range of the WD mass obtained from the UV light curve fitting. The lower limit corresponds to the case of a very large mass-loss rate of −6 −1 1 × 10 M⊙ yr , while the upper limit is the extreme case of no wind mass-loss (see Kato et al. 2011). b Values at log T (K)=3.90. c We adopt Vpeak = 8.59 for the optical flat peak. Theoretical absolute V - magnitudes are calculated as MV = Mbol − 0.17. This equation gives a relation between E(B − V ) and d for a specified model, Model 1, which is depicted in Figure 2. There is another possible way of fitting. In 1979, PU Vul showed a spectral type of F0 I without emission lines, and its magnitude was about V = 8.87 (see Figure 8). If we take a bolometric correction typical for F0 I/II, BC(V )=0.13 (Straizys & Kuriliene 1981), we have a larger distance modulus (m − M)V = 14.44 for the same Model 1. This case is also plotted in Figure 2. We have another distance-reddening relation from the UV 1590 A˚ light curve fitting, i.e.,
− 2.5 log F1590(obs) = −2.5 log F1590(model) +Aλ + 5 log (d/1 kpc). (3)
Here Aλ = R1590 E(B − V ) and we adopt R1590=8.3 (Fitzpatrick & Massa 2007). Seaton (1979)’s for- mula gives a similar value of 7.9. Figure 1(d) shows −13 −1 −2 −1 F1590(obs) = 6.1 × 10 erg s cm A˚ at the −10 UV 1590 A˚ peak, whereas F1590(model) = 1.77 × 10 erg s−1 cm −2 A˚−1 with an assumed distance of d = 1 kpc. Substituting these values into equation (3), we get a relation 6.15=8.3 × E(B − V ) + 5 log (d/1kpc) (4) for Model 1. Figure 2 also shows Equation (4) with two additional lines in the both sides which represent a pos- sible 15% error in the light curve fitting. This error is a summation of the accuracy of the absolute flux calibra- tion of IUE (∼ 5%) and possible contamination of emis- sion/absorption line contribution in the region of 1590 Fig. 1.— UV light curves for four narrow bands at, a) 1350 A,˚ A,˚ which we assumed to be 10 %. b) 1455 A,˚ c) 1490 A,˚ and d) 1590 A.˚ Theoretical light curves Combined these two fittings, i.e., Equations (2) and are also shown for an assumed distance of 1 kpc (with right-side − axis) and no absorption; They are 0.6 M⊙ WDs with the chemi- (4), we obtain E(B V )=0.37 and d =4.1 kpc, which cal composition of the envelope X = 0.7 and Z = 0.01 with four are plotted by a black X-mark (the middle one among different optically-thin wind mass-loss rates; Dash-dotted curves: −7 −1 −7 −1 the three Xs). If we assume a different WD mass, we 4 × 10 M⊙yr . Solid curves: 5 × 10 M⊙yr (Model 1). Dot- − −7 −1 −7 −1 get a different relation between E(B V ) and d, because ted curves: 6 × 10 M⊙yr . Dashed curves: 8 × 10 M⊙yr . Short vertical lines in panels b), c), and d) show the period of the MV is different for a different WD mass model. The two second eclipse at the optical V band between JD 2,449,270 and X-marks in the left/right sides in Figure 2 indicate the 2,449,610. Among the observational data, the open circles denote intersection of the two extreme cases of MWD =0.52 and the ones with low accuracy because they were observed with a short 0.72 M⊙, corresponding to the lowest and highest WD exposure time (< 1000 s) or it is obtained from very noisy spectra. The red arrows indicate the epoch of the UV maximum in each masses (see Table 2). wavelength band. For different sets of chemical composition, we also get different intersections which are shown by different symbols in Figure 2. From these points we see that E(B − V ) = 0.37 is almost independent of the WD PU Vul–evolution of WD, RG, and nebula 5
Fig. 2.— Distance-reddening relation of PU Vul. The distance-reddening relations obtained from the optical light curve fitting of Model 1; black solid line: (m − M)V = 14.20, i.e., Equation (2); black dotted line: (m − M)V = 14.44. The red solid line represents the UV 1590 A˚ light curve fitting of Model 1 (Equation (4)). The two red dotted lines beside the line represent possible ±15% errors in absolute UV flux. The distance-reddening relation derived from the K-magnitude fitting (Equation (7)) is depicted by the green solid line with ±0.2 mag error lines in both sides. The central black cross indicates the intersection of the UV and optical fluxes of Model 1. The crosses in both sides represent the intersections for MWD = 0.52 (left) and 0.72 M⊙ (right) WD models with the chemical composition of X = 0.7 and Z = 0.01, i.e., the lowest and highest WD masses in Table 2. Other models are depicted by the different symbols: blue filled circles for Model 2, green open squares for Model 3, red triangles for Model 4. The intersections for the same models but for different extinction law are also plotted by blue symbols: (RV , R1590)=(2.40, 6.29) for HD185418, (2.48, 8.03) for HD197702, and (2.91, 8.84) for BD +35 4258. The same symbol indicates the same chemical composition and the middle point of the three same symbols corresponds to the models in Table 1. The name of each star is indicated beside the corresponding group of points with first few letters. The open star mark represent d=4.7 kpc and E(B − V ) = 0.3. See Section 3.1 for more detail. mass or chemical composition. This is because we use HD 197702, and (2.91, 8.84) for BD +35 4258. Using the same response (passband) functions to derive MV these values, we obtain the intersection from Equations and log F1590(model) from blackbody spectrum of each (1) and (3), which are also shown in Figure 2. These model, and therefore, the ratios of the two values are extinction estimates strongly depend on the adopted ex- common in all the models. As a result, these two equa- tinction curve. tions yield a common value of E(B − V ) independent of Thus, we could not accurately determine the distance the model. On the other hand, the distance depends on and E(B −V ) from the light curve fittings of UV/optical the WD mass and chemical composition (X), because a bands. more massive WD/smaller X has a larger photospheric luminosity, which results in a larger distance. In this 3.2. Optical Color Excess way, we could not determine the distance only from the A direct estimate of the color excess E(B − V ) can be light curve fittings. We can constrain the distance corre- derived from the comparison of observed B − V colors sponding to a permitted range of the WD mass as listed and spectral types of the hot component during 1979- in Table 1. 1983, i.e., at the optical maximum when strong emis- It should be noted that Galactic interstellar absorption sion lines were still absent. In particular, we have calcu- has very large uncertainty around the average value we lated one-month averaged B − V and U − B colors from adopted (see e.g. Fitzpatrick & Massa 2007). Unfortu- the published photometry (Belyakina et al. 1982a, 1985, nately, the extinction curve are not known in PU Vul, 1990; Kolotilov 1983; Margrave 1979; Mahra et al. nor in the stars close to its same sight line. The closest 1979; Whitney 1979; Bruch 1980; Chochol et al. 1981; stars are relatively far away; towards HD 185418 and HD Purgathofer & Schnell 1982) for several epochs when 197702 , both ∼ 11 deg away from PU Vul, and towards the spectral classification of PU Vul was made (Kolotilov BD +35 4258, ∼ 15 deg away. The values of (RV and 1983; Belyakina et al. 1984; M¨urset & Nussbaumer R1590) are (2.40, 6.29) for HD 185418, (2.48, 8.03) for 1994, and references therein). Table 3 shows the one- 6 Kato et al.
TABLE 3 Color excess in optical
a b c b c Date Sp. Type
a These spectral types are taken from Kolotilov (1983), Belyakina et al. (1984), and M¨urset & Nussbaumer (1994, and references therein). b The average B − V and U − B color indices are calculated using the data from Belyakina et al. (1982a, 1985, 1990); Kolotilov (1983); Margrave (1979); Mahra et al. (1979); Whitney (1979); Bruch (1980). c The intrinsic color indexes of supergiants, (B − V )0 and (U − B)0, are from Straizys (1992). d The UBV colors in May 1979 (Chochol et al. 1981) and in August 1981 (Purgathofer & Schnell 1982) show some sys- tematic offset with respect to those from other sources, and are displayed separately. month averaged B − V and U − B colors and spec- regular variables pulsating in the fundamental mode, tral classification corresponding to each epoch. Assum- ing that the nova envelope of PU Vul had a typical MK = −3.51 × (log P (day) − 2.38) − 7.25, (5) spectral type, we can estimate the extinction with the with an error of ∼ 0.2 mag (Whitelock et al. 2008). For comparison to the intrinsic color index corresponding the 218 day pulsation, we get the absolute K magni- − to its spectral type (Straizys 1992). The B V and tude of MK = −7.10 ± 0.2. During the 1980 eclipse U − B colors of PU Vul are in good agreement with the average K mag changes from 6.26 mag to 6.51 those of bright supergiants for 1979–81, and the av- mag (Belyakina et al. 1985) and its average value is +0.12 erage ratio of E(U − B)/E(B − V )= 0.66−0.14 esti-
TABLE 4 Temperature and Radius of Hot Componenta
b c Date JD Spectral Ion V Th Mbol Lh Rh Method 2,400,000+ type (K) (L⊙) (R⊙) 04/1979 43980 A7 II 8.84 7900 -5.36 11070 56 [1] 05/1979 43991 F0 I 8.93 7400 -5.23 9820 60 [1] 07/1979 44070 F0 I 8.84 7400 -5.32 10670 63 [1] 12/1979 44222 F3 I 8.78 6900 -5.41 11590 75 [1] 08/1981 44834 F5 I 8.55 6500 -5.66 14590 95 [1] 09/1981 44873 F5 I 8.50 6500 -5.65 14510 95 [2] 06/1982 45147 F5 I 8.50 6500 -5.71 15280 97 [1] 09/1982 45229 F5-8 I 8.67 6300 -5.57 13430 97 [1] 11/1982 45290 F3-4 I 8.40 6800 -5.79 16440 92 [1] 12/1982 45320 F0 I 8.43 7400 -5.73 15560 76 [1] 07/1983 45533 F0 I 8.39 7400 -5.77 16140 77 [1] 10/1984 45989 A3 I 8.55 8900 -5.77 16140 53 [1] 06/1985 46232 A3 I 8.52 8900 -5.80 16600 54 [1] 09/1986 46690 A2 I 8.72 9200 -5.67 14720 48 [1] 01/1988 47176 – S+ – 10000d – – – – 06/1988 47328 – N+ – 15000d – – – – 10/1988 47438 – N+2 – 35000 -5.43 11800 3.0 [3] 10/1988 47438 – N+2 – 29000 -5.49 10704 4.4 [3a] 05/1989 47666 – C+3,N+3 – 40000 -5.47 12230 2.3 [3] 05/1989 47666 – C+3,N+3 – 48000 -5.47 15440 1.8 [3a] 05-09/1989 47730 – C+3,N+3 – 48000 -5.70 15140 1.8 [4] 04/1990 47795 – O+3 – 55000 -5.81 16750 1.4 [4] 07/1990 48088 – Ne+2 – 41000d -5.64 14320 2.4 [4] 11/1990 48217 – He+2 – 65000 -5.65 14500 0.95 [5], SWP40155 04/1991 48352 – He+2 – 65000 -5.64 14350 0.94 [5], SWP41299 09/1991 48522 – He+2 – 67000 -5.59 13710 0.87 [5], SWP42536 10/1991 48559 – He+2 – 70000 -5.55 13230 0.78 [5], SWP42937/8 08/1992 48858 – He+2 – 77000 -5.67 14660 0.68 [5], SWP45415 06/1995 49886 – Ne+4 – 97000 -5.58 13540 0.41 [6] 06/1995 49886 – Ne+4 – 97000 -5.68 14860 0.43 [4] 06/1996 50237 – He+2 – 90000 -5.31 10570 0.42 [5], SWP57322/3 06/1996 50237 – – – 90000 -5.42 11700 0.36 [4] 09/1996 50342 – He+2 – 83000 -5.05 8300 0.44 [5], SWP58251/2 09/2001 52154 – Fe+6 – 100000 -4.68 5940 0.26 [6] 09/2001 52154 – Fe+6 – 100000 -5.42 11700 0.36 [4] 26/3/2003 52818 – Fe+6 – 165000 -4.97 7730 0.11 [4] 9/4/2004 53105 – Fe+6 – > 99000 – – – – 04/2004 53110 – – – 150000e -4.97 7720 0.13 [4] 07/2006 53930 – O+5 – > 114000 – – – – 07/2006 53930 – O+5 – 150000e -4.70 6030 0.11 [4] 06/2011 55740 – – – 150000e -5.02 8090 0.13 [4] a We assume d = 4.7 kpc and E(B − V ) = 0.30. b Highest ionization stage. c Methods used in deriving the results (see Section 4 for details). [1] Supergiant phase method; [2] Integration of SED; [3] Black body fit to a short wavelength IUE spectrum with T as a free parameter; and [3a] with T from the highest ionization stage observed; [4] M¨urset & Nussbaumer (1994) method based on UB observations of the nebular phase; [5] analysis of He II1640 emission line and ultraviolet continuum; [6] based on He II 4686 emission line flux. d Ionization stage and Th taken from M¨urset & Nussbaumer (1994). e Arbitrary assumed. and the differences in the results give an idea about the the temperatures and bolometric corrections for A-F su- uncertainties of these methods. pergiants from Straizys & Kuriliene (1981), and adopt The third column of Table 4 shows the spectral classifi- M⊙(bol)=4.75 for the absolute bolometric luminosity of cation adopted from Kolotilov (1983), Belyakina et al. the Sun. (1984), and M¨urset & Nussbaumer (1994, Table 3), and The hot component luminosity in September 1981 (JD the fifth column shows the average of observed V mag- 2 444 873) have been estimated directly by integrating nitudes (Kolotilov 1983; Belyakina et al. 1982a, 1985, the spectral energy distribution (SED) from ultravio- 1990) of PU Vul during the optical maximum, 1979– let to infrared. To get the SED we have combined 1986. The outbursting component of PU Vul showed the very long exposure IUE spectra (SWP 15110, LWR spectra similar to that of an early F-type supergiant, 11627 and LWR 11628) from 27 September 1981 with gradually evolving towards an A supergiant. Since there Belyakina et al. (1985) spectrophotometry performed is no strong nebular contribution during this phase, we on 25 September 1981 and JHK photometry obtained have assumed that the spectral type is an appropri- on 22 September 1981. The SED has been corrected ate indicator for the effective temperature and bolo- for the reddening. The resultant bolometric magnitude metric correction, and that the observed V magnitude is mbol,0 = 7.71, which derives the absolute bolometric (Kolotilov 1983; Belyakina et al. 1982a, 1985, 1990) magnitude Mbol = −5.65 with the distance d =4.7 kpc. represents that of the hot component. We have adopted This value, −5.65, shows an excellent agreement with the 8 Kato et al.
highest ionization potential (IP) observed in the IUE spectra (JD 2447438–795) and published op- tical spectra (Munari & Zwitter 2002; Yoo 2007; Tatarnikova & Tatarnikov 2011). We used the relation Th/1000 ∼ IP (eV) found by M¨urset & Nussbaumer (1994). For two epochs of JD 2452154 and 2452818, Th is derived from the ratios of Hβ, He II 4686 and He I 5876 emission line fluxes published by Tatarnikova & Tatarnikov (2011) and Luna & Costa (2005), respectively. At two epochs of 1988 and 1989, the hot component parameters have been derived by fitting a blackbody to the short wavelength (λ . 1590 A)˚ part of the spectrum obtained by combining SWP34405, SWP34406, and SWP34407 for JD 2447438, and SWP36301, SWP36302 and SWP36304 for JD 2447666. Fig. 3.— Development of the temperature (open triangles and the left ordinates) and radius (filled circles and the right ordinates) of After 1996, in the absence of IUE spectra, Lh has been the hot component (WD) of PU Vul, taken from Table 4. Two red derived from the UB mag observed by Belyakina et al. upward arrows indicate lower limits of temperature. Model lines (2000) and by Shugarov et al. (2011) with the method denote the photospheric temperatures and radii of the 0.6 M⊙ WD with X = 0.7 and Z = 0.01 for five different wind mass-loss rates. proposed by M¨urset & Nussbaumer (1994). This −7 −1 Dash-dotted lines: 4 × 10 M⊙ yr . Thick solid lines: 5 × method assumes that after subtraction of the contri- −7 −1 −7 −1 10 M⊙ yr (Model 1). Dotted lines: 6 × 10 M⊙ yr . Thin bution from the RG, the optical magnitudes contain a −7 −1 −7 −1 solid lines: 7 × 10 M⊙ yr . Dashed lines: 8 × 10 M⊙ yr . direct contribution from the hot star and an indirect Three black downward arrows indicate the central times of the contribution from the nebulae. Thus, an accurate es- 1980, 1994, and 2007 eclipses. timate of the RG contribution is especially important. The RG companion is classified to be a spectral type average value, −5.66 in August 1981, derived from the of M6 (Section 5.1), so its contribution to UB magni- observed V mag and spectral type (see Table 4). tudes can be neglected. In fact, the B − V and U − B We have also used this SED to estimate the bolomet- colors (Shugarov et al. 2011) suggest that the contin- ric correction corresponding to this particular date, in uum is still dominated by the nebular emission, in agree- September 1981. We obtain V0 = 7.57 from the SED. ment with the optical spectra showing only faint flat Thus, the bolometric correction is calculated as BC(V )= continuum and strong emission lines (e.g. Yoo 2007). mbol,0 − V0 = 0.14. On the other hand, Belyakina et al. As described later (Sections 5 and 6 and Figure 8), (1985) obtained V = 8.45 on JD 2444873, which is the summation of the WD and nebular contributions corrected to be V0 = 7.52 with an extinction of 3.1 × dominates the V light curve, although it shows a clear E(B − V )=0.93. Combining this with mbol,0 =7.71, we ∼ 0.5 mag pulsation owing to the RG. Therefore, we can get BC(V )=0.19. These BC(V ) values are somewhat safely use the method of M¨urset & Nussbaumer (1994). larger than BC(V )=0.08 corresponding to F5 I spectral M¨urset & Nussbaumer (1994) also provided the bolo- type estimated at this epoch. The difference may reflect metric corrections to UBV mag of hot component for a the lower density in the nova envelope than that in the wide range of hot component temperature, Th. These brightest F-type supergiants. In the present work, we bolometric corrections were derived by model calcula- use BC(V )=0.17, the mean value of 0.14 and 0.19. tions with hot component temperature and nebular den- For the nebular phase, whenever possible, the temper- sity as free parameters. Although the RG in PU Vul is ature of the hot component (WD), Th, has been esti- similar to a Mira component of D-type symbiotic sys- mated from the equivalent width of the He II 1640 emis- tems, we have decided to use the bolometric corrections sion line measured from IUE spectra (identified in the for S-types because the U − B color of PU Vul during last column of Table 4). Although the high resolution the nebular phase is similar to that predicted by the HST/GHRS spectrum taken in October 1994 (the 1993/4 M¨urset & Nussbaumer (1994) model for S-types, and eclipse egress) suggest ∼ 20% of O I]1641 line contribu- the electron density derived for the nebular phase is sim- tion to the He II fluxes derived from lower resolution ilar to the values characterizing the other S-type systems spectra, the O I]1641 line is not visible in the well ex- (Luna & Costa 2005). posed high resolution spectra SWP45417 and SWP57730 At JD 2449886 and JD 2452154, the luminosity of taken before and after the eclipse, respectively. There- the hot component, Lh has been calculated from the fore, we assume a negligible contribution of O I] to our published He II 4686 fluxes (Andrillat & Houziaux 1995; measurements of the He II 1640 line. The luminosity Tatarnikova & Tatarnikov 2011), assuming a blackbody of the hot component, Lh, has been calculated from the spectrum with T and that the He II lines are produced II h He 1640 flux, assuming blackbody (Th) and that the by photoionization followed by recombination (case B). He II lines are produced by photoionization followed by Our estimated temperature and radius are plotted in recombination (case B). Lh has been also estimated from Figure 3. This figure also shows theoretical models for the IUE flux at 1350 A,˚ assuming that it is emitted by the 0.6 M⊙ WD with the composition of X = 0.7 and blackbody (Th). At most epochs in Table 4 these two val- Z = 0.01, i.e., the same models as in Figure 1. The ues agree with each other, and a mean value is adopted higher the mass-loss rate, the faster the evolution. All of for the final Lh. these models show more or less good agreement with our At several epochs, Th has been derived from the PU Vul–evolution of WD, RG, and nebula 9
Fig. 4.— Evolution of the hot component of PU Vul in the HR diagram. Red open circles are our observational estimates, taken from in Table 4. Pairs connected by a line segment indicate the es- timates obtained for the same day data but with different methods. Fig. 5.— Observational years (two digits except 1979) are attached beside A close up view of the first eclipse. Our model light the point. Various types of lines denote loci of theoretical models. curve is indicated by the red solid line, which is a summation of Solid lines indicate, from upper to lower, Model 4 (red), Model 3 the eclipsed WD photosphere, a constant nebular emission of V = (green), Model 1 (black), and Model 2 (brown). A dashed line de- 14.0, and the RG photosphere with a sinusoidal oscillation around notes a 0.7 M⊙ WD with X = 0.7 and Z = 0.01. Four dotted lines V = 13.6 (green dash-dotted line). The mideclipse on JD 2,444,532 denote 0.5 M⊙ WD models with different radius and chemical com- is indicated by a downward arrow. See text for more details. positions. From upper to lower, a cold WD (the Chandrasekhar radius) with X = 0.5 and Z = 0.02, a cold WD with X = 0.7 and companion. The bottom magnitude of V ∼ 13 during the Z = 0.01 (upper) which is almost overlapped with a cold WD with eclipse seems to be a bit higher than that of a late type X = 0.7 and Z = 0.02 (lower). The lowest line denotes a hot WD with X = 0.7 and Z = 0.02. Dots represent the epoch when nu- M-giant, which suggests the presence of a weak emission clear burning extinguishes. Arrows indicate evolution timescales of source which was not occulted. Before going to our model Model 1; from the beginning to log Tph (K)=4.0, and from log Tph construction, we need to examine the magnitude of the (K)=4.0 to 5.05, i.e., 8.7 yr and 9.6 yr, respectively. M-giant companion. observational estimates. It should be noticed that the The spectral classification of the RG companion is theoretical values are those of a blackbody photosphere. estimated to be M3–M7, but better estimates are ob- Even though, they show good agreement with the IUE tained in longer wavelength bands rather than in the flux (Figure 1) and also with the estimates obtained with optical because of contamination by nebular emission. quite different methods (Table 4). M¨urset & Schmid (1999) obtained M6–7, using the Figure 4 shows the HR diagram of the hot component. bands in near IR, i.e. λ & 8000 A.˚ Belyakina et al. This figure shows theoretical tracks of the 0.5, 0.6 and (1985) derived a similar type, M6.5, during the 1980 0.7 M⊙ WDs for various chemical compositions. The eclipse. This value is uncorrected for the faint nebula observational estimates are also in good agreement with (V ∼ 14), so there may be some fluctuations by ±1 in our 0.6 M⊙ models. the spectral type. Therefore, we regard M6 as a reason- 5. LIGHT CURVE MODELS OF ECLIPSES able average spectral type of the M-giant. The magnitude of the RG can be estimated from its Now we present light curve models of the first (1980) K-band magnitude. Belyakina et al. (1985) obtained and second (1994) eclipses. Here we assume spherical
TABLE 5 Eclipse Light Curve Model
Subject 1st eclipse 2nd eclipse Units mideclipse ... 4,532 9,447 JD 2,440,000+ total duration (D) ... 508 345 day totality (d) ... 254 343 day mean RG magnitude ... 13.6 13.6 mag amplitude of RG luminosity ... 75 % 65 % total amplitude of RG in maga ... 2.1 1.7 mag amplitude of RG radius ... 7 % 3 % Rc/a ... 0.246 0.22 Rh/a ... 0.070 0.0007 nebular emission ... 14.0 see Fig. 6 mag a V (min)-V (max) source are free parameters. Figure 5 shows a close-up view of the first eclipse and our light curve model. A model light curve, that produces a better fit to the observed magnitude data, is shown in Figure 5. We ob- tain the total duration of the eclipse D = 508 days, the ∗ totality d = 254 days, and Rc /a = (D + d)/(2πPorb) = 0.244, where a is the separation of the two stars, Porb is the orbital period in units of day, and the asterisk denotes the specific radius, because it depends on the timing of pulsations at the ingress/egress. The equilibrium radius of the pulsating RG is Rc = 0.247 a. The RG radius is smaller than the equilibrium radius at the second and third contacts, i.e., 0.93 and 0.96 times the equilibrium ∗ radius, we obtain Rc/a slightly larger than Rc /a. A bottom magnitude is obtained as a combination of the RG equilibrium magnitude and the nebular emission. An equilibrium magnitude of the RG darker than V = 13.8 does not reproduce the wavy bottom shape, even if we assume a very large amplitude of the luminosity. A combination of the RG equilibrium magnitude of V = 13.6 – 13.8 and a nebular emission of V ∼ 14.0 yield a better fitting as shown in Figure 5. Here we assume Fig. 6.— A close up view of the second eclipse. Observa- the RG equilibrium magnitude to be V = 13.6 and the tional data are taken from Kolotilov et al. (1995) (crosses) and nebular emission V = 14.0. Yoon & Honeycutt (2000) (open circles). The red solid line indi- cates our composite light curve which is a summation of the four For the oscillation of the RG radius, a good fitting is components, i.e., the pulsating RG (green dash-dotted line), WD obtained for amplitudes of the radius ∆Rc/Rc = 0.06– (magenta solid line), constant “nebula 1” emission of V = 14.0 0.08. For a larger amplitude ∆Rc/Rc & 0.1, we cannot (black solid line), and gradually decreasing “nebula 2” emission find a good shape of light curves, because a wavy struc- which is eclipsed by 25 % (brown solid line). The RG is pulsating around its mean magnitude of V = 13.6. The mideclipse on JD ture appears during the ingress and egress. Here, we 2,449,447 is indicated by a downward arrow. adopt ∆Rc/Rc =0.07. Our fitting parameters are summarized in Table 5, spectively. However, the wavy bottom shape in Figure 5 showing the mideclipse time, i.e., the time when the RG is consistent with the RG pulsation. center comes just in front of the WD, the total duration of eclipse (D), totality (d), apparent magnitude of the 5.2. The Second (1994) Eclipse RG at its equilibrium state, amplitude of the RG lumi- PU Vul began to decline in 1987 from the flat max- nosity in linear scale ∆LV /LV , corresponding to the to- imum and reached V ∼ 11.5 just before the second tal amplitude in magnitude (difference between the max- eclipse in 1994. The bottom magnitude of the second imum and minimum magnitudes), amplitude of the RG eclipse is V ∼ 11.8 (see Figure 6), 1.8 mag brighter than radius, the ratio of the RG radius to the separation a, and that of the 1980 eclipse. This eclipse is considered to the ratio of the WD radius to a. Note that the RG mag- be total, because the continuum UV radiation, which nitude at equilibrium is not the arithmetic mean of the has a WD origin, was disappeared during the eclipse maximum and minimum magnitudes, because we assume (Nussbaumer & Vogel 1996; Tatarnikova & Tatarnikov a sinusoidal variation in the luminosity (linear scale), not 2009). Therefore, the excess flux (∆V ∼ 1.8 mag) is a in the magnitude (logarithmic scale). contribution of hot nebulae. Garnavich (1996) supposed that this eclipse is par- Nussbaumer & Vogel (1996) analyzed UV spectra of tial because of a non-flat bottom. Vogel & Nussbaumer the hot nebulae and found that highly ionized lines dis- (1992) explained this non-flat bottom shape as a total appeared during the eclipse and recovered after that, eclipse, but contaminated by two nebular emissions that whereas low-ionized nebular lines were hardly affected. cause the flux excess in the early half and later half, re- This means that the high excitation lines were emitted PU Vul–evolution of WD, RG, and nebula 11 from a region close to the WD and the low-ionized neb- ular lines are emitted from an outer extended region. In other words, the nebulae are also partially occulted. Thus, there are three sources of emission: the pulsating RG, totally occulted WD, and partially occulted nebu- lae. For the RG, we assume a similar model as in the first eclipse, i.e., the RG is pulsating around the equilib- rium magnitude of V = 13.6 but maybe with different amplitudes of the luminosity and radius, which are fit- ting parameters. For the WD emission, we take Model 1, which is shown in Figure 6 (labeled as WD). We assume two sources of nebular emission, one is a constant com- ponent (labeled “nebula 1”) assumed in the first eclipse, i.e., V = 14.0. The other is a decreasing component which is partially occulted during the second eclipse (la- beled “nebula 2”). Its luminosity and decline rate are also parameters in order to obtain the best fit. Figure 6 shows the resultant light curve. The ampli- tude of the luminosity is determined to be 65 % and that of the radius is 3 %. For the nebula 2 component, we found that a 25 % occultation of the nebula 2 emission yields the best fit. We see that our composite light curve represents the temporal change of the optical data. These fitting parameters are summarized in Table 5. It is difficult to obtain the WD radius from the light curve fitting because the ingress and egress of the second Fig. 7.— Light curve of PU Vul for the period JD 2,447,000– eclipse is very steep, which indicates the eclipsed object 2,451,000 (upper part) and JD 2,453,500–2,457,500 (lower is very small. Therefore, we fixed the WD radius to be part). Observational data are taken from Kolotilov et al. (1995)(crosses), Yoon & Honeycutt (2000)(small open circles), Rh/a =0.0007, which corresponds to 1.0R⊙ for a circular Klein et al. (1994)(squares), Kanamitsu et al. (1991)(open orbit of a binary consisting of a 1.0M⊙ RG and a 0.6M⊙ stars), and Iijima (1989)(middle size open circles). For the WD. This assumption has no effects in determining the lower part, observational data are taken from AAVSO (dots) other parameters. and All Sky Automated Survey (ASAS) (crosses). Downward arrows indicate the central times of the eclipses, JD 2,449,447 and 2,454,362. Short vertical lines indicate epochs of the pulsation 5.3. M-giant Pulsation and 3rd Eclipse maxima of the M giant assuming a period of 218 days. Figure 7 shows a periodic modulation of the V mag- nitude, which becomes prominent in the later phase of TABLE 6 the outburst where the WD component becomes dark. Radii of the Cool and Hot Componentsa This modulation is unclear in the flat maximum except the first eclipse (Figures 5), because the hot component b c RG mass a Rc(1st) Rc(2nd) Rh(1st) is dominant. We regard that this modulation is caused (M⊙) (R⊙) (R⊙) (R⊙) (R⊙) by a pulsation of the RG. 3.0 ... 1860 459 413 131 We obtained the pulsation period to be 218 days, as- 2.0 ... 1670 411 370 118 suming that the period is unchanged from the first eclipse 1.5 ... 1550 383 345 109 until 2010. This 218 day period can reproduce well both 1.0 ... 1420 350 315 100 the first and second eclipses as shown in Figures 5 and 0.8 ... 1360 335 301 95.6 0.6 ... 1290 318 286 90.9 6. Chochol et al. (1998) obtained a 217 day period and 0.4 ... 1210 299 269 85.5 Shugarov et al. (2011) obtained a 217.7 day period. Our a value is consistent with these periods. A circular orbit and a 0.6 M⊙ WD are assumed. b (1st) means the value obtained for the 1st eclipse Figure 7 shows that one of the minima of the RG pul- c (2nd) from the 2nd eclipse sation accidentally coincides with the time expected for the third eclipse in 2007 indicated by an arrow. This lar orbit, we calculated the binary separation a from Ke- narrow dip is not the third eclipse of the WD, because pler’s third law, a3 = G(P /2π)2(M + M ). The the duration is too short, and the WD had already be- orb WD RG resultant radii of the RG and WD are listed in Table 6 come very dark in the optical band (see Figure 8), and an as well as a for various RG masses. Here we assume a 0.6 occultation of the WD hardly changes the total bright- M⊙ WD mass. Estimated RG radii (270 – 460 R⊙) seem ness of PU Vul. Shugarov et al. (2011) showed that the to be a little bit larger than those of low mass M giant U magnitude is clearly eclipsed in the third eclipse, but stars, which will be discussed in Section 7 (Discussion). the V magnitude is not. Our interpretation is consistent For the hot component, we obtain a radius of R /a = with theirs. h 0.07 for the first eclipse, that corresponds to Rh ∼ 85– 130 R⊙ as shown in Table 6. For the second eclipse, we 5.4. Radii of Cool/Hot Components have fixed the WD radius to be Rh/a =0.0007, because In Sections 5.1 and 5.2 we have obtained Rc/a and the ingress and egress are too steep to determine the Rh/a for the first and second eclipses. Assuming a circu- radius. Thus, it is not listed in the table. The steep 12 Kato et al. decline/rise suggest Rh/a < 0.001 which corresponds to the orbit. Then the width of eclipse by the RG is so Rh < 1–2 R⊙. We can only say that the radius of the wide that a whole period of the orbital phase is partially hot component reduced by a factor of 100 or more. eclipsed as shown by the blue dashed line in Figure 8. In Section 4 we have already shown that the WD pho- This increase in the brightness (U, B, and V ) also sug- tosphere had shrunk by about two orders of magnitudes gests that the hydrogen shell-burning on the WD is still between the first and second eclipses, from both the ob- on-going. servational estimates and theoretical models (see Figure 3). The above radius estimates from the eclipses are very 7. DISCUSSIONS consistent with these estimates in Figure 3. This is the 7.1. Comparison with Other Works on Eclipses first time that the shrinkage of a nova WD photosphere has been measured by eclipse analysis. Garnavich (1996) estimated the relative size of the cool component to be Rc/a =0.28 for the first eclipse and 6. COMPOSITE OPTICAL LIGHT CURVE 0.22 for the second eclipse, assuming symmetric shapes of ∗ Figure 8 shows an observational light curve of PU Vul the eclipses. Our corresponding values are Rc /a = 0.24 from the beginning of the outburst until 2010. It also de- and 0.22, respectively. The difference in the first eclipse picts our theoretical composite light curve that consists is explained from the difference in the totality. Assuming of three components, the WD, RG, and nebulae. The that the bottom base line at the first eclipse was V = 11.8 WD component, in which we use Model 1, well repro- from the second eclipse, Garnavich get a larger totality duces the observed UV light curve (Figure 8a) as well than ours. Thus, Rc/a becomes larger than ours. In as the optical light curve until 1989. After 1989, PU the second eclipse our Rc/a is essentially the same as Vul entered a nebular phase and emission-lines dominate Garnavich’s, because the radius oscillation of the RG has the spectra (Iijima 1989; Kanamitsu et al. 1991). Our little effects due to small amplitude (3 %). WD model does not include line-emission formed outside For the hot component, Garnavich (1996) estimated the photosphere, thus the V -light curve (red solid line) Rh/a =0.1 for the first eclipse, which is consistent with decays much faster than the observed one. For the RG our value of Rh/a = 0.07, considering difficulty of ac- component, we assume that the equilibrium magnitude curate fitting with the scattered data. For the second is constant, V = 13.6, throughout the outburst as we eclipse Garnavich’s value Rh/a = 0.02 is much larger did in the first and second eclipses in Section 5. This than our value of Rh/a =0.0007. This difference comes V = 13.6 is indicated by the green horizontal solid line mainly from the different data sets. Garnavich used the in Figure 8b. AAVSO data that show slower decline/increase at the For the nebular emission, we assume two components: ingress/egress than those in Figure 6. These AAVSO one is a constant component of V = 14.0 as depicted data, however, can be also fitted by a more steep light by the dash-three-dotted line (nebula 1) in Figure 8b. curve that yields Rh/a < 0.01. Therefore, in the both We assumed this component uneclipsed at all during the cases, we can say that the radius of the hot component first and second eclipses as shown in Figures 5 and 6. had decreased at least by a factor of ten between the first We suppose this nebula 1 emission originated from the and second eclipses. RG cool wind, partially ionized by the radiation from Garnavich (1996) concluded that the RG radius the hot component. As this emission is faint, it domi- shrunk by 21 % between the first and second eclipses, i.e., nated the total magnitude only in the first eclipse, so we from Rc/a =0.28 to 0.22. Our values are much smaller, have no information on its magnitude whether it changed 10 % (from Rc/a = 0.246 to 0.22), but the shrinkage or not. Therefore, we assumed that this component is of the radius seems to be real because we cannot find a constant. Tatarnikova & Tatarnikov (2011) found the parameter set for the same RG radius between the two Raman scattered O VI 6830 line in the optical spectra eclipses. We will discuss the shrinkage of the radius in taken in mid 2006 and later. This indicates the presence the next subsection. of neutral hydrogen, i.e., the RG cool wind. As the WD The orbital period of PU Vul is estimated from the is still hot, a part of the RG cool wind may be ionized. mideclipses of the first and second eclipses to be 4915 So we reasonably suppose this component is still present. days (13.46 yr) (see Table 5). The orbital period ± The other nebula is originated from the WD, the shape was obtained as 4918 8 days (Kolotilov et al. 1995), ± ± of which is represented by the blue dashed line (neb- 4900 100 days (Nussbaumer & Vogel 1996), 4900 9 ula 2). This component started at the epoch when the (Garnavich 1996), 4897 days (Shugarov et al. 2011), photospheric temperature of the WD increased to log T assuming symmetric shapes of the eclipses. Our anal- (K)=4.0 (open square in Figure 8). This WD-origin com- ysis first includes a radius oscillation and the resulted ponent was first discussed by Nussbaumer et al. (1988), non-symmetric shapes of eclipses. However, these effects who concluded that the nebular emission is of WD-origin cause only several days off from the symmetry center be- because the relative abundances of C, N, and O are close cause of small amplitudes of the radial oscillations. This to those of classical novae but different from symbiotic is the reason why our new period is close to the previous stars. This component was eclipsed during the second estimates. eclipse as in Figure 6. 7.2. Recently, Shugarov et al. (2011) reported that all of Comparison with Other Evolution Calculations the U, B, and V magnitudes are gradually rising after the Figure 4 shows the evolution timescale of Model 1, third eclipse while the mean value of the I magnitude is 18.3 yr from the beginning of the outburst to log Tph almost constant. This indicates that the WD-origin neb- (K)=5.05. If we do not include the optically-thin wind ular component is relatively centrally condensed around mass-loss, this becomes 46 yr, and the total duration of the WD and, at the same time, widely spread out over the outburst, from the beginning to the extinguish point PU Vul–evolution of WD, RG, and nebula 13
Fig. 8.— Optical and UV light curves of PU Vul. (a) UV light curve. Large open circles denote the IUE UV 1590 A˚ band (the same as those in Figure 1d). The solid curve denotes the UV light curve of Model 1. The scale is in units of 10−13 erg s−1 cm−2 A˚−1. (b) Optical light curve. Middle size open circles are V magnitudes during the flat phase listed in Table 4. See Kato et al. (2011) for the other observational data. The red solid and dotted lines indicate optical and bolometric light curves of Model 1. The large open square indicates −7 −1 the epoch at log Tph(K)=4.0 when the optically thin wind of 5 × 10 M⊙ yr started in our model. The magenta solid line indicates a composite light curve of the WD (red solid line), RG at the mean luminosity V = 13.6 (horizontal green solid line), emission of a constant component at V = 14.0 (“nebular 1”: blue dash-three-dotted line), and a variable component (“nebular 2”: blue dashed line). Downward arrows indicate the mideclipses. We suppose that the “nebula 2” is eclipsed by the RG companion after 2002 (denoted by ’wide eclipse’). of nuclear burning, is 130 yr. Using a hydrodynami- by Cassisi et al. (1998) and Piersanti et al. (1999, cal code Prialnik & Kovetz (1995) calculated multicycle 2000) who calculated shell flashes on low-mass WDs us- nova evolution models for various WD masses and ac- ing a spherical symmetric hydrostatic code with the Los cretion rates. For a 0.65 M⊙ WD and a mass accretion Alamos opacity. Cassisi et al.’s (1998) models show that −7 −1 rate of 1 × 10 M⊙yr , no optically thick wind mass- the envelope extends only down to log Tph (K)=4.5–4.7 loss arose. They obtained the total duration of the nova for a 0.5 M⊙ WD with mass accretion rates of 2 and −8 −1 outburst to be t3bol=155–176 yr, depending on the core 4 ×10 M⊙yr . Also in Piersanti et al. (2000), the temperature, where t3bol is the time during which the temperature decreases down to log Tph (K) =4.1–4.2 only bolometric luminosity drops by 3 mag. For lower accre- in a few exceptional cases. Such high-temperature shell −8 −1 tion rates (≤ 10 M⊙yr ) strong optically thick winds flashes may be observed as a UV flash. In other words, occur which shorten the total duration. Their total du- these calculations do not represent realistic nova out- ration is very consistent with our 0.6 M⊙ WD model, bursts in which the surface temperature drops to log Tph considering the different definition of the end point of a (K) < 4.0 at the optical peak. This suggests that their shell flash; Our definition is for the hydrogen burning ex- numerical code has some difficulties in calculating real- tinguish point (depicted by the dot in Figure 4), whereas istic nova outburst models. Prialnik & Kovetz’ is for t3bol time which comes later It should be pointed out that the above three than our extinguish point, thus gives a longer timescale works are obtained with the Los Alamos opacity, than ours. not with the OPAL opacity (Rogers & Iglesias 1992; Following the referee’s suggestion we discuss the work Iglesias & Rogers 1993, 1996), which has been widely 14 Kato et al. used in stellar evolution codes including nova outbursts. (Glass et al. 2003). The fundamental pulsation We are puzzled by the remark in Cassisi et al. that ’the mode of Mira variables corresponds to this sequence. Los Alamos opacities are very similar to the OPAL opac- With the distance modulus of LMC, 18.39 ± 0.05 ities’ (see the last sentence of Section 4 in Cassisi et al. (van Leeuwen et al. 2007), we obtain Mbol = −4.05 1998). It is well known that the OPAL opacities have for P = 218 day. Therefore, if the RG companion fol- a strong peak at log T (K) ∼ 5.2, while the Los Alamos lows the PL relations of Miras, its absolute luminosity opacities do not (For comparison with these opacities in is Mbol = −4.05, i.e., log L = 3300 L⊙. Photometric a nova envelope, see Figure 15 in Kato & Hachisu 1994). studies on a large number of stars indicate another PL This strong peak causes substantial changes in nova out- relation, parallel to the above relation, but about one bursts, e.g., acceleration of optically thick winds, and as magnitude brighter. This sequence corresponds to the a results, nova evolutions had significantly changed (e.g., first overtone of pulsation in semi-regular variables. In compare hydrodynamical calculations of nova outbursts this case, we have Mbol = −5.05, i.e., log L = 8300L⊙. in Prialnik (1986) obtained with the Los Alamos opacity The spectral type of the companion is estimated to be with Prialnik & Kovetz (1995) with the OPAL opacity). M6 (see Section 5.1). The temperature calibration for In a less massive WD (. 0.6M⊙), no optically thick wind late M giants is relatively well established, and various is accelerated, but internal structures of the envelope are groups give similar values. In particular, Richichi et al. significantly different; a density inversion layer appears (1999) give Teff = 3240±75K and 3100±80 K for M6 and corresponding to the peak of the OPAL opacity (see Fig- M7 giants, respectively, whereas Van Belle et al. (1999) ure 7 in Kato et al. 2011). In order to make a reliable report 3375 ± 34 K and 3095 ± 29 K for M6 and M7, re- outburst model of PU Vul, we need to use the OPAL spectively. So, Teff = 3200 ± 100 K for the M6–7 giant in opacity, not the Los Alamos opacity (see also Discussion PU Vul seems very reasonable. The radius then becomes in Kato 2012). R = 187 ± 12R⊙. For the second PL relation we have ± 7.3. R = 296 19R⊙. Comparing these radii with the ones Pulsating RG Companion in Table 6, we may conclude that the pulsation of the As described in the previous subsection, our eclipse RG companion is consistent with the fundamental mode analysis shows that the RG radius decreased by ∼ 10 % rather than the first overtone, because the visual photo- between the first and second eclipses. This radius may sphere is much larger than the stellar radius (Rc ∼ 1.8 not be the photospheric radius of the RG defined in near times the stellar radius, that is, Rc ∼ 330 R⊙ for the IR bands, but the radius of a thick TiO atmosphere, fundamental mode: Reid & Goldston 2002). which is transparent in K-band but opaque in V -band. If the RG pulsation is in the first overtone, the abso- In the pulsating RG atmosphere, the temperature de- lute magnitude is about 1 mag brighter than in the fun- creases in the expanding phase, which accelerates TiO damental mode as described above, thus the distance is molecule formation, resulting in a large opacity in the 1.6 times larger, i.e., d =4.7 kpc ×1.6=7.4 kpc. Such a optical region, which causes a deep minimum in the op- large distance is inconsistent with the optical light curve tical light curve. The radius, that we obtained from the fittings, because E(B − V ) becomes too small or nega- eclipses in V -band, corresponds to the radius of the TiO tive ( see black solid/dotted lines in Figure 2), thus we atmosphere. We call this the ”visual photosphere” af- cannot construct a consistent model among the optical, ter Reid & Goldston (2002). This radius could be much UV 1590 A,˚ and extinction. Note that the ”IR” line in larger than the photospheric radius usually defined with Figure 2, i.e., Equation (5) is for the fundamental mode K-band observation. Therefore, it is very likely that our and the corresponding line for the first overtone is in the visual photosphere in Table 6 is larger than the RG ra- right outside of the figure. Therefore, we may conclude dius in K-band. that the pulsation is a fundamental mode. As shown in Section 5.3 the pulsation period of 218 Next, we estimate the RG mass using a theoretical re- days had not changed between the first and second lation obtained from radial-pulsations. It is well known eclipses. The unchanged pulsation period means that that the pulsation constant, Q = P pM/R3, is insensi- the internal structure of the RG had not changed, so the tive to stellar structure, here M is the stellar mass in K-band photospheric radius should be the same. On the units of M⊙, R the radius in units of R⊙, and P the pul- other hand, our analysis clarified that the pulsation am- sation period in units of day. Therefore, the pulsation plitude in V -band decreased from 75 % to 65 %, and mass is given by also the amplitude of the radius decreased (see Table 5). This suggests that the radius of the visual photosphere Q2R3 decreased as the amplitudes of the luminosity and ra- M = 2 . (9) dius had decreased. This can be understood as follows; P The TiO atmosphere is pushed outward in an expanding Numerical calculations show that Q = 0.06 – 0.08 for phase, and it pushed far outward when its amplitude is the fundamental mode, and Q =0.03 – 0.04 for the first larger. Therefore, a larger amplitude results in a larger overtone (e.g., Xiong, & Deng 2007). Using the radius visual photosphere. estimated above and P = 218 day, we can estimate the We can estimate the RG radius, using the period- RG mass (pulsation mass) to be M = 0.5–0.9 M⊙ for luminosity (PL) relations of Mira/semi-regular variables. both of the fundamental and first overtone modes. The The bolometric luminosity of LMC Mira variables follows 0.8 M⊙ is consistent with the visual photospheric radius a PL relation of of 335 R⊙ in Table 6 for the fundamental mode. A different way to estimate the RG mass comes from mbol = (−3.06 ± 0.26) log P + (21.50 ± 0.61), (8) binary evolution theory. A WD of mass ∼ 0.6 M⊙ cor- where P is the pulsation period in units of day responds to a ∼ 2.0 M⊙ zero-age main-sequence star in PU Vul–evolution of WD, RG, and nebula 15 the initial-final mass relation derived from observation 8. CONCLUSIONS ∼ (e.g., Table 3 in Weidemann 2000), or a 3 M⊙ in Our main results are summarized as follows: stellar evolution calculation for binaries (Umeda et al. 1. We present new estimates of the temperature and 1999). Then, the companion star should be smaller than radius of the hot component from a very early phase of − 2 3 M⊙, because the more massive component in a bi- the outburst (1979) until 2011. These are very consistent nary evolves first. These values are consistent with the with our theoretical model of outbursting WDs based above estimate derived from the pulsation theory. on thermonuclear runaway events without optically thick winds. 2. We analyzed the first (1980) and second (1994) eclipses, assuming sinusoidal variations of the brightness 7.4. X-ray observation and radius of the RG. Both of the eclipses are explained as a total eclipse of the WD occulted by the pulsating PU Vul becomes a supersoft X-ray source in the RG. Between the first and second eclipses, both of the later phase of the outburst when the surface tempera- components shrank in size. The radius of the hot com- ture of the WD becomes high enough to emit X-rays. ponent decreases from ∼ 100R⊙ to ∼ 0.1R⊙, which is Kato et al. (2011) estimated the supersoft X-ray flux, very consistent with our theoretical model. but it was very uncertain because the long-term evolution 3. We are able to construct a composite optical light of the temperature depends on the assumed optically- curve that consists of four components of emission, i.e., thin mass-loss rate as well as the possible absorption the WD photosphere, hot nebulae surrounding the WD, due to the RG cool winds. In the present work, we RG photosphere, and nebulae possibly originating from confirm that the nuclear burning still continues and the RG cool winds. thus the WD currently evolves toward a supersoft X- 4. We have estimated the extinction and distance with ray phase. We also showed that the binary system various methods, that is, the light curve fittings of optical contains two different origins of nebulae, i.e., nebula 1 and UV 1590 A˚ bands based on our WD model, direct es- comes from the RG cool-wind and nebula 2 from the timates of color excess, and using K-magnitude and P-L WD hot-wind. This cool-wind origin nebula absorbs relation of the pulsating RG companion. These different a part of the supersoft X-ray flux, because the neb- methods yield consistent values of E(B − V ) ∼ 0.3 − 0.4. ula is partially neutral (Rayleigh scattering in 1991- and d = 4 − 5 kpc. We adopt E(B − V )=0.3 and 1993:Tatarnikova & Tatarnikov (2009); Raman scat- VI d =0.47 in the present paper as representative values. tered O lines since 2006: Tatarnikova & Tatarnikov 5. We interpret the recent long term evolution of V (2011)). Therefore, the supersoft X-ray flux should vary magnitude in terms of eclipse of the hot nebula surround- with the binary phase, i.e., the flux is minimum when ing the WD: the V magnitude gradually decreased from the RG is in front of the WD and maximum when the 2002 and reached a minimum in 2007 and is now in a re- WD is in front of the RG. The UBV light curves of PU covering phase in 2012. This means that hydrogen burn- Vul (Shugarov et al. 2011) show such a long term vari- ing is still ongoing. Therefore, we suggest X-ray obser- ation with the orbital phase. As mentioned in Section 6 vations around June 2014 to detect supersoft X-rays. we explain this variation as an eclipse of nebula 2 by the RG (and also possibly by the nebula 1). Therefore, the supersoft X-ray flux may also show a similar long-term The authors wish to express great thank to S. Shugarov variation. We expect that the X-ray flux will be max- and A. Tatarnikova for providing photometric data as imum when the UBV flux is maximum. If the orbit is well as for discussion on recent observations of PU circular, the next maximum will be in June 2014, and it Vul. We are very grateful to M. Takeuti and N. Mat- is a good chance to detect supersoft X-rays. sunaga for providing information and valuable discussion SMC 3 is a symbiotic star consisting of a massive of pulsating red giants. We also thank to the anony- WD and an M-giant, which attracts attention in relation mous referee for useful comments that helped to im- to the progenitor of type Ia supernovae (Hachisu et al. prove the manuscript. We also thank A. Cassatella and 2010). Its supersoft X-ray flux and B-magnitude R. Gonz´alez-Riestra for useful discussion, the American show similar long-term variations in the orbital phase Association of Variable Star Observers (AAVSO) and (Sturm et al. 2011). Sturm et al. analyzed the X-ray All Sky Automated Survey (ASAS) for archival data variation, but could not give a definite explanation about of PU Vul. This research has been supported in part the X-ray variability. We could, however, explain this X- by the Grant-in-Aid for Scientific Research (20540227, ray and B-magnitude variations in terms of wide eclipses 22540254) of the Japan Society for the Promotion of Sci- because it is similar to the UBV variations of PU Vul. ence and by the Polish Research Grant No. N203 395534.
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